This sounds exactly like Tunnie's problem. The battery positive terminal has a thick wire crimped onto it which leads across the front of the engine to the alternator and starter motor. The rest of the car is fed from a cable bolted to the terminal which leads to the positive distribution box that lays on top of the battery.
All the current to feed the car electrical system and charge to the battery must therefore pass through the crimped connection. In Tunnie's case we only had about 13v across the battery with the engine running, regardless of revs. In the minute or two we spent measuring it, the battery terminal got too hot to touch. The insulation on the wire had also discoloured.
I'm not sure if you will be able to see the change in resistance with a multimeter. We are talking fractions of an ohm here but it's worth a try. The other test is to look at the battery voltage with engine running, and a little bit of electrical load (headlights, climate, etc), and again wiggle the cable. The fact that it gets hot is indication enough that there's a bad connection, though.
This wire also carries the current to the starter motor so, not only does it prevent the battery charging fully, it also reduces the current available to the starter motor.
As to a remedy I wouldn't bother trying to re-crimp it. You need a serious crimping tool to make connections that big and they'll probably fail in the same way. In addition, the end of the wire will have been cooked and will have a higher resistance anyway, as a consequence.
I would suggest either replacing the whole section of cable with one in good condition or cutting the wire 6" or so back from the connector, joining a new section of cable using a brass ferrule and solder, insulating the joint well with heat shrink sleeving and tape, and then fitting a new battery terminal with screw terminals.
You'll find all the required parts here
http://www.vehicle-wiring-products.co.uk or in a motor factors.
Cheers,
Kevin